Test Statistics and P-value

Question

Among n babies born in a certain city, 51% were boys. Suppose we want to test the hypothesis that the true probability of a boy is 1/2. Conduct the appropriate test for this situation, using a non-directional alternative. Show all necessary work, state the hypothesis statements, compute the test statistic, P-value, and provide a concluding statement in the context of this problem.
Consider two cases: (a) n = 1,000 (b) n = 5,000

Answer 1

When choosing an n say n=1000 you are actually testing a proportion, p ( not to be confused with the p-value which is something different.)

 

H_{0 :} p = .50

 

H_{1 :} p ≠ .50

 

the test proportion (statistic) was p = .51

 

when testing a proportion µ = np   and  σ = √npq  changes to 

 

                                       µ = p = .5     and    σ = √pq/n = √(.5)(.5)/1000

 

you must choose and appropriate value of the significance level α

 

CONTINUED-------

 

(FYI I teach classes in statistics so I don't know if the techniques I am giving here are what you instructor is looking for.)

 

Picking a non-directional α = .05 would give a cutoff value of .975 (normal distribution)

 

Calculating the p-value (from .51) would be z=(.51-.50)/(√(.5)(.5)/1000)=.01/.0158 =.63

                                                               p-value of .63 is .7357

 

Since .7357 < .975 we do not reject null hypothesis (assuming all my calculations are correct.)

 

This procedure really requires much more interactive explanation.

 

 

b) now try n=5000

 

 

Lilly, Again I don't know if this technique is what you instructor was looking for. It's unfortunate your school does not offer any outside of class help.

 

As I said I teach classes in statistics and probability. If you want one-one tutoring I would certainly offer my services. If you are interested or have any questions please send me a message.

 

Dr. F.